There are many approaches to reducing the presence of noise in digital images. In order to minimize the required amount of computing resources needed, most commercial approaches to noise reduction in digital images are based on using very small regions of the image for each set of noise reduction computations. One of the simplest approaches with practical value is to use a 3×3 square region of pixels centered on the pixel to be noise reduced. This region is known in the literature as a pixel neighborhood or a support region. With only nine pixel values in the neighborhood available for computational purposes, a variety of algorithms can be used for producing a noise-reduced pixel value without undue burden on most computational resources. If the predominant nature of the noise signal being reduced consists of isolated erroneous pixel values, this pixel neighborhood size is generally sufficient for most noise reduction schemes. If the noise signal is more complex, however, and has clumps of erroneous pixel values that are several pixels wide in extent, the 3×3 square region of pixels will probably be insufficient for adequate noise reduction. The 3×3 square region will still permit the reduction of isolated erroneous pixel values, but will be largely ineffective on larger clumps of noise, especially if said clumps are larger than the 3×3 square region itself. The obvious solution is to increase the size of the noise reduction support region. This is generally a viable alternative up to the point at which the additional burden on the computational resources becomes unacceptable. Unfortunately, it is common for the computational limits of the system to be reached before the support region has been allowed to expand to the desired dimensions for adequate noise reduction.
A solution to these computational limitations is to decompose the image to be noise reduced into a series of images with varying spatial resolutions. In the literature this is described as performing a Laplacian pyramid decomposition. The process is simple. The starting image at its initial spatial resolution is referred to as a base image. A copy of the base image is blurred and then subsampled to a lower resolution. This lower resolution image is a new base image at the next level of the pyramid. This process can be repeated until there are insufficient pixels for any subsequent subsampling operation. A residual image is associated with each base image. In order to create the residual image for a given level of the pyramid, the lower resolution base image from the adjacent level of the pyramid is upsampled and subtracted from the base image at the given level of the pyramid. This difference image is called a residual image. A fully decomposed image consists of a set of base images and corresponding residual images. The advantage of this representation of the image is that small support region image processing operations can be applied to each of the base and/or residual images so as to produce the same results as using a very large support region operation at the original image resolution. In the case of noise reduction, this permits the use of, for example, 3×3 square regions at each level of the pyramid to effectively noise reduce larger and larger clumps of noise. Once the individual images of the pyramid have been processed, the image decomposition process is essentially run in reverse order to reconstitute the full resolution image.
There are many examples of related prior art in this field. U.S. Pat. No. 5,488,374 (Frankot, et al.) discloses a pyramid decomposition-based noise reduction method that uses simple linear noise filters tuned for each pyramid level. U.S. Pat. No. 5,526,446 (Adelson, et al.) teaches using steerable noise filters within a pyramid decomposition-based architecture. U.S. Pat. No. 5,729,631 (Wober, et al.) reveals using Wiener filters and discrete cosine transforms to noise reduce in the spatial frequency domain within the framework of a pyramid decomposition. U.S. Pat. No. 5,963,676 (Wu, et al.) describes using wavelet decomposition to accomplish its pyramid decomposition and then using an edge-preserving smoothing filter to perform noise reduction at each pyramid level. U.S. Patent Application Publication No. 2002/0118887 (Gindele) discloses a pyramid decomposition-based noise reduction method that uses modified sigma filters tuned for each pyramid level.
A significant problem with existing noise reduction methods is that they are still very computationally intensive when either the image to be noise reduced is very large (e.g. 14 million pixels) or the noise signal is very large with respect to the genuine image signal. When the image consists of a large number of pixels, the required computing resources scales directly with the number of pixels to noise reduce. Using a pyramid decomposition architecture addresses this liability to some extent. When the amount of noise present is large, then generally more complex noise reduction algorithms, such as median filters, must be imbedded into the pyramid architecture to avoid seriously degrading genuine image information. A double jeopardy situation can exist when both circumstances are present.
What is needed is a method that provides the noise reduction capability of a pyramid decomposition approach without relying on complex noise reduction operations at each level of the pyramid so as to keep the required computational intensity to a minimum. This method must still noise reduce in an effective manner when dealing with images with high levels of noise.